The problem is:
O2 sensors, even the best of the best in the best situations and best etc are still more than 4% off
The colder they are, the more off they are going to be
O2 sensors can't function in high flow environments, like ~3k rpm + - ie, they can't react fast enough
O2 sensors can't distinguish between a little and a lot lean/rich - they only know one or the other
So the colder they are, the more error they have, and the slower they react to changes. Meaning, by the time a cold o2 sensor realizes your lean, you've already burned up your motor.
So if it's in the proper place, or using a heated one, you lessen the risks and increase their efficiency.
Cycling oxygen sensors are a requirement for closed loop operation. There is generally another parameter in the tuning establishing closed loop countdown vs engine temp. (longer warmup countdown when engine is cold)
Oxygen sensors do not cycle until they are warmed up.
Oxygen sensors can cycle several times per second.
Oxygen sensors will work at any RPM, once long term fuel trims are established, accurate fueling correction is realtime and essentially seamless. Although at high rpm's (more accurately high manifold pressure), fueling switches to open loop power enrichment mode and no longer takes active feedback from the oxygen sensors.
Oxygen sensors are not used in situations where your motor can 'burn up', only in low power closed loop operation. Motors can safely run a very lean AFR while cruising, although due to increased combustion temperatures this creates very high levels of nitrogen oxides (NOx) and is not permitted.
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